DiSSECT

Name	secp112r1 (secg/secp112r1, wtls/wap-wsg-idm-ecid-wtls6)
Category	secg
Description	A randomly generated curve. [SEC2v1](https://www.secg.org/SEC2-Ver-1.0.pdf) states 'E was chosen verifiably at random as specified in ANSI X9.62 [1] from the seed'.
Field	Prime (0xdb7c2abf62e35e668076bead208b)
Field bits	112
Form	Weierstrass $y^{2} = x^{3} + a x + b$
Param $a$	0xdb7c2abf62e35e668076bead2088
Param $b$	0x659ef8ba043916eede8911702b22
Generator $x$	0x09487239995a5ee76b55f9c2f098
Generator $y$	0xa89ce5af8724c0a23e0e0ff77500
Simulation seed	0xf50b028e4d696e676875615175290472783fb1

Order	0xdb7c2abf62e35e7628dfac6561c5
Cofactor	0x1
$j$ -invariant	0xadad8cacc8dd210422960337beca
Trace $t$	-0xfa868edb84139
Embedding degree $k$	0xdb7c2abf62e35e7628dfac6561c4
CM discriminant	-0x36cfb7fe7ccf1fcdd86299e26837b

$discriminant ()$
cm_disc	-0x36cfb7fe7ccf1fcdd86299e26837b
factorization	['0x35', '0x108bfd95477d520dd70f469b4aef']
max_conductor	0x1

$twist_order (d e g = 1)$
twist_cardinality	0xdb7c2abf62e35e56d80dd0f4df53
factorization	None

$twist_order (d e g = 2)$
twist_cardinality	0xbc2dad5ce3bc2b4e238afa969c17239d881126f438ddec4b3334c915
factorization	None

$kn_factorization (k = 1)$
(+)factorization	['0x2', '0x3', '0x3', '0xc319098dad3be23024550b04c8b']
(+)largest_factor_bitlen	0x6c
(-)factorization	['0x2', '0x2', '0x29', '0x35b', '0x661aedbb7d5022c18e27c86b']
(-)largest_factor_bitlen	0x5f

$kn_factorization (k = 2)$
(+)factorization	['0x1b6f8557ec5c6bcec51bf58cac38b']
(+)largest_factor_bitlen	0x71
(-)factorization	['0x3', '0x5', '0xe1ac9e43', '0x21327c01eb7594f0408d']
(-)largest_factor_bitlen	0x4e

$kn_factorization (k = 3)$
(+)factorization	['0x2', '0x2', '0x2', '0x2', '0x5', '0x5', '0x7', '0xb', '0x23d5', '0x329c383bd', '0xc5c80d71f0951']
(+)largest_factor_bitlen	0x34
(-)factorization	['0x2', '0x3d', '0x65', '0xdae1209d9de8d986bec337737']
(-)largest_factor_bitlen	0x64

$kn_factorization (k = 4)$
(+)factorization	['0x3', '0x10f', '0x7b5', '0x15ef9', '0x1a29d35dc42e3165066d']
(+)largest_factor_bitlen	0x4d
(-)factorization	['0x7', '0xbf', '0x3d7', '0x2bc7454b5e27ebe791b8054d']
(-)largest_factor_bitlen	0x5e

$kn_factorization (k = 5)$
(+)factorization	['0x2', '0x3b03', '0xbacb', '0xcbe50f12060ba33525a8d']
(+)largest_factor_bitlen	0x54
(-)factorization	['0x2', '0x2', '0x2', '0x3', '0xd', '0x1a99d0c6672e7b', '0x21d9b95ed452b7']
(-)largest_factor_bitlen	0x36

$kn_factorization (k = 6)$
(+)factorization	['0x5c9', '0x11fb3', '0xca8e0140ba7107bbc9debd']
(+)largest_factor_bitlen	0x58
(-)factorization	['0x4f', '0xa7', '0xfa97b', '0x1a1ae40a21a23ce2031cf']
(-)largest_factor_bitlen	0x51

$kn_factorization (k = 7)$
(+)factorization	['0x2', '0x2', '0x3', '0x1d', '0x49d', '0x2c9f6ff', '0x7ffa9c5', '0xafb80554121']
(+)largest_factor_bitlen	0x2c
(-)factorization	['0x2', '0x5', '0x11', '0x8b', '0x17b', '0xb3e316477c4288dbafb7985']
(-)largest_factor_bitlen	0x5c

$kn_factorization (k = 8)$
(+)factorization	['0x5', '0xd', '0x3b3', '0x611', '0x13429a2fd89d2f80a383dc3']
(+)largest_factor_bitlen	0x59
(-)factorization	['0x3', '0x3', '0xb', '0x4a881', '0x3ceb84848401affbc764ded']
(-)largest_factor_bitlen	0x5a

$torsion_extension (l = 2)$
least	0x3
full	0x3
relative	0x1

$torsion_extension (l = 3)$
least	0x8
full	0x8
relative	0x1

$torsion_extension (l = 5)$
least	0x8
full	0x8
relative	0x1

$torsion_extension (l = 7)$
least	0x3
full	0x6
relative	0x2

$torsion_extension (l = 11)$
least	0x78
full	0x78
relative	0x1

$torsion_extension (l = 13)$
least	0x18
full	0x18
relative	0x1

$torsion_extension (l = 17)$
least	0x8
full	0x10
relative	0x2

$conductor (d e g = 2)$
ratio_sqrt	0xfa868edb84139
factorization	['0x5', '0xd', '0x16f', '0x28d', '0x10dd2c33']

$conductor (d e g = 3)$
ratio_sqrt	0xda86ffa9a447e1aa04c5621f21da
factorization	['0x2', '0x1d', '0x1d', '0x71cb', '0x4ad317ad0aa745ac7240ef']

$conductor (d e g = 4)$
ratio_sqrt	0x1aca551801c30a182dfa456d09258edc0663ee6d7d
factorization	['0x3', '0x5', '0xd', '0x3d', '0x16f', '0x1e7', '0x28d', '0x111f2cf', '0x10dd2c33', '0xe1843d15', '0x155adf0e73f']

$embedding ()$
embedding_degree_complement	0x1
complement_bit_length	0x1

$class_number ()$
upper	0x2e766b29b64c3406
lower	0x1

$small_prime_order (l = 2)$
order	0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length	0x1

$small_prime_order (l = 3)$
order	0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length	0x1

$small_prime_order (l = 5)$
order	0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length	0x1

$small_prime_order (l = 7)$
order	0x6dbe155fb171af3b146fd632b0e2
complement_bit_length	0x2

$small_prime_order (l = 11)$
order	0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length	0x1

$small_prime_order (l = 13)$
order	0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length	0x1

$division_polynomials (l = 2)$
factorization	[['0x3', '0x1']]
len	0x1

$division_polynomials (l = 3)$
factorization	[['0x4', '0x1']]
len	0x1

$division_polynomials (l = 5)$
factorization	[['0x4', '0x3']]
len	0x1

$volcano (l = 2)$
crater_degree	0x0
depth	0x0

$volcano (l = 3)$
crater_degree	0x0
depth	0x0

$volcano (l = 5)$
crater_degree	0x0
depth	0x0

$volcano (l = 7)$
crater_degree	0x2
depth	0x0

$volcano (l = 11)$
crater_degree	0x0
depth	0x0

$volcano (l = 13)$
crater_degree	0x0
depth	0x0

$volcano (l = 17)$
crater_degree	0x2
depth	0x0

$volcano (l = 19)$
crater_degree	0x0
depth	0x0

$isogeny_extension (l = 2)$
least	0x3
full	0x3
relative	0x1

$isogeny_extension (l = 3)$
least	0x4
full	0x4
relative	0x1

$isogeny_extension (l = 5)$
least	0x2
full	0x2
relative	0x1

$isogeny_extension (l = 7)$
least	0x1
full	0x6
relative	0x6

$isogeny_extension (l = 11)$
least	0xc
full	0xc
relative	0x1

$isogeny_extension (l = 13)$
least	0x2
full	0x2
relative	0x1

$isogeny_extension (l = 17)$
least	0x1
full	0x10
relative	0x10

$isogeny_extension (l = 19)$
least	0x14
full	0x14
relative	0x1

$trace_factorization (d e g = 1)$
trace	-0xfa868edb84139
trace_factorization	['0x5', '0xd', '0x16f', '0x28d', '0x10dd2c33']
number_of_factors	0x5

$trace_factorization (d e g = 2)$
trace	-0xfa868edb84139
trace_factorization	['0x3', '0x3d', '0x1e7', '0x111f2cf', '0xe1843d15', '0x155adf0e73f']
number_of_factors	0x6

$isogeny_neighbors (l = 2)$
len	0x0

$isogeny_neighbors (l = 3)$
len	0x0

$isogeny_neighbors (l = 5)$
len	0x0

$q_torsion ()$
Q_torsion	0x1

$hamming_x (w e i g h t = 1)$
x_coord_count	0x3a
expected	0x38
ratio	0.96552

$hamming_x (w e i g h t = 2)$
x_coord_count	0xc26
expected	0xc24
ratio	0.99936

$hamming_x (w e i g h t = 3)$
x_coord_count	0x1be4c
expected	0x1bd28
ratio	0.99744

$square_4p1 ()$
p	0x1
order	0x1

$pow_distance ()$
distance	0x2483d5409d1ca189d720539a9e3b
ratio	6.01082
distance 32	0x5
distance 64	0x5

$multiples_x (k = 1)$
Hx	0x9487239995a5ee76b55f9c2f098
bits	0x6c
difference	0x4
ratio	0.96429

$multiples_x (k = 2)$
Hx	0xaa8728a0279bd6d44e8c99c573e7
bits	0x70
difference	0x0
ratio	1.0

$multiples_x (k = 3)$
Hx	0x71b29d6bd4cc566539bf5644a154
bits	0x6f
difference	0x1
ratio	0.99107

$multiples_x (k = 4)$
Hx	0xd41907b39931dffa6103ffbc8c2c
bits	0x70
difference	0x0
ratio	1.0

$multiples_x (k = 5)$
Hx	0xa29c1051c271f7338c08444f4783
bits	0x70
difference	0x0
ratio	1.0

$multiples_x (k = 6)$
Hx	0xa0f134694e5c834e7c00b9674359
bits	0x70
difference	0x0
ratio	1.0

$multiples_x (k = 7)$
Hx	0x1c715b2f7acf3dd1e2dbc2d296fc
bits	0x6d
difference	0x3
ratio	0.97321

$multiples_x (k = 8)$
Hx	0x8ebafec5962bc4aa17f901910ce
bits	0x6c
difference	0x4
ratio	0.96429

$multiples_x (k = 9)$
Hx	0x268f1146825d33758a143e8c663b
bits	0x6e
difference	0x2
ratio	0.98214

$multiples_x (k = 10)$
Hx	0xd4153672fa25b82d85c3fb51962e
bits	0x70
difference	0x0
ratio	1.0

$x962_invariant ()$
r	0x29e49e36f941c1b2dc1fb82b5bce

$weierstrass ()$
a	0xdb7c2abf62e35e668076bead2088
b	0x659ef8ba043916eede8911702b22

Curve detail

Definition

Characteristics

Traits